Chef and the stones

Chef has two piles of stones with him, one has n1 stones and the other has n2 stones. Fired up by boredom, he invented a game with the two piles. Before the start of the game Chef chooses an integer m. In the j-th move: - He chooses a number xj such that 1 ≤ xj ≤ m, and removes xj stones from both the piles (this is only possible when both the piles have ≥ xj stones). - The number chosen must